Find the exact value of sin345^circ using the sum/difference identity. sin345^circ =square (sqrt (6)+sqrt (2))/(4) (-sqrt (6)-sqrt (2))/(4) (sqrt (6)-sqrt (2))/(4) (sqrt (2)-sqrt (6))/(4) 2+sqrt (3) -2-sqrt (3) 2-sqrt (3) sqrt (3)-2

Question

Answer 1

To find the exact value of

using the sum/difference identity, we can use the identity for the sine of a difference of angles:

Let

and

. Then

.Using the known values of

,

, and

, we have:

Therefore, the exact value of

is

.

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